Finite Group Databasebeta

← #16784514

Subgroups — #16784514

Order 3328.

774 conjugacy classes of subgroups; only the 192 normal subgroups are shown.

normal subgroups only

This group has 774 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13130768C211yesmaximal, characteristic, complemented
2C42×#1057C211yesmaximal, characteristic, complemented
3C2×D4⋊#1057C214yesmaximal, complemented
4#127×Dic13C211yesmaximal, characteristic
5C2×C13×#127C411yescharacteristic
6C2×D4×Dic13—22no—
7C2×D4×Dic13C2212yes—
8C2×C4⋊#1057—22no—
9C2×C4⋊#1057C2212yes—
10C2×C4×#1057—22no—
11C2×C4×#1057C2212yes—
12#11718882—22no—
13#11718882C412yes—
14#11718596C411yescharacteristic
15C42×Dic13C2211yescharacteristic
16D4⋊#1057—28no—
17C22×D4×C13—22no—
18C22×D4×C13C2×C412yes—
19C23×Dic13—22no—
20C22×#1057—22no—
21C22×#1057—22no—
22C13×#127—22no—
23C13×#127C814yescomplemented
24C2×C42×C13C2×C411yescharacteristic
25C2×C22⋊Dic13—24no—
26C2×C22⋊Dic13—22no—
27D4×Dic13—24no—
28D4×Dic13—24no—
29D4×Dic13—44no—
30D4×Dic13—44no—
31C2×C4⋊Dic13—22no—
32C2×C4⋊Dic13C2×C412yes—
33C2×C4×Dic13C2×C411yescharacteristic
34C2×C4×Dic13D412yes—
35C2×C4×Dic13D412yes—
36C2×C4×Dic13C2311yescharacteristic
37C4⋊#1057—24no—
38C4⋊#1057—44no—
39C4×#1057—28no—
40C4×#1057—22no—
41C4×#1057D414yescomplemented
42#9638—131nomaximal, Sylow
43C24×C13—22no—
44C2×D4×C13—28no—
45C2×D4×C13—24no—
46C2×D4×C13—22no—
47C2×D4×C13—24no—
48C2×D4×C13—44no—
49C2×D4×C13—44no—
50C2×D4×C13C2×C814yes—
51C22×C4×C13C22⋊C412yes—
52C22×C4×C13C22×C411yescharacteristic
53C22×Dic13—22no—
54C22×Dic13—42no—
55C22×Dic13—42no—
56C22×Dic13—44no—
57C22×Dic13—44no—
58C22×Dic13C22⋊C412yes—
59C22×Dic13C2×D411yescharacteristic
60C22×Dic13C2×D411yescharacteristic
61C2×#1057—28no—
62C2×#1057—24no—
63C2×#1057—42no—
64C2×#1057—44no—
65C42×C13C2×C812yes—
66C42×C13M1612yes—
67C22⋊Dic13—48no—
68C22⋊Dic13—44no—
69C4⋊Dic13—24no—
70C4⋊Dic13—44no—
71C4×Dic13—24no—
72C4×Dic13—22no—
73C4×Dic13D814yes—
74C4×Dic13SD1614yes—
75C4×Dic13C2×D412yes—
76C4×Dic13#4112yes—
77C4×#127—131no—
78#1842—131no—
79C42×C8—131no—
80C2×D4⋊C8—134no—
81C23×C13—24no—
82C23×C13—42no—
83C23×C13—42no—
84C23×C13—44no—
85C23×C13—44no—
86C23×C13C2×C22⋊C411yescharacteristic
87D4×C13—28no—
88D4×C13—416no—
89D4×C13—44no—
90C2×C4×C13C22⋊C814yes—
91C2×C4×C13#10214yes—
92C2×C4×C13#10414yes—
93C2×C4×C13C4×D412yes—
94C2×C4×C13C22×C811yescharacteristic
95C2×C4×C13C2×M1611yescharacteristic
96C2×C4×C13#13112yes—
97C2×Dic13—22no—
98C2×Dic13—22no—
99C2×Dic13—22no—
100C2×Dic13—42no—
101C2×Dic13—44no—
102C2×Dic13—84no—
103C2×Dic13—82no—
104C2×Dic13—82no—
105C2×Dic13#10214yes—
106C2×Dic13#12112yes—
107C2×Dic13#12411yescharacteristic
108C2×Dic13#12711yescharacteristic
109C2×Dic13C2×D812yes—
110C2×Dic13C2×SD1612yes—
111#1057—28no—
112#1057—82no—
113C2×#127#26111yescharacteristic
114C2×C4×D4—132no—
115C2×C4×D4—262no—
116C2×C4⋊C8—132no—
117C2×C4⋊C8—262no—
118C2×C4×C8—132no—
119C2×C4×C8—262no—
120#390—132no—
121#390—262no—
122#384—131no—
123C43—131no—
124D4⋊C8—268no—
125C22×C13—44no—
126C22×C13—48no—
127C22×C13—82no—
128C22×C13—82no—
129C22×C13—84no—
130C22×C13#39011yescharacteristic
131C22×C13C2×C22⋊C811yescharacteristic
132C22×C13#40811yescharacteristic
133C22×C13C2×#10212yes—
134C22×C13C2×#10412yes—
135C4×C13D4⋊C818yescomplemented
136C4×C13C8×D412yes—
137C4×C13#43612yes—
138Dic13—22no—
139Dic13—24no—
140Dic13—82no—
141Dic13#48612yes—
142Dic13#49211yescharacteristic
143Dic13#49311yescharacteristic
144C22×D4—22no—
145C22×D4C2×#26112yes—
146C23×C4—262no—
147C22×C8—262no—
148C22×C8—262no—
149#127—22no—
150#127#105714yescomplemented
151C4×D4—264no—
152C4×D4—264no—
153C4×D4—524no—
154C4×D4—524no—
155C2×C4⋊C4—132no—
156C2×C4⋊C4—262no—
157C2×C22⋊C4—262no—
158C2×C22⋊C4—264no—
159C2×C42—132no—
160C2×C42—131no—
161C2×C42—132no—
162C2×C42—131no—
163C2×C42C2×#26111yescharacteristic
164C4⋊C8—264no—
165C4⋊C8—524no—
166C4×C8—134no—
167C4×C8—262no—
168C4×C8—268no—
169C2×C13—84no—
170C2×C13C2×D4⋊C812yes—
171C2×C13#149212yes—
172C2×C13#195411yescharacteristic
173C2×C13#195711yescharacteristic
174C2×C13#196211yescharacteristic
175C24—22no—
176C2×D4—28no—
177C2×D4—24no—
178C2×D4—24no—
179C2×D4—22no—
180C2×D4—44no—
181C2×D4—44no—
182C2×D4C2×#105714yes—
183C22×C4—131no—
184C22×C4—131no—
185C22×C4—132no—
186C22×C4—262no—
187C22×C4—522no—
188C22×C4—522no—
189C22×C4—524no—
190C22×C4—524no—
191C22×C4C22⋊#26112yes—
192C22×C4C22×#26111yescharacteristic
193C2×C8—264no—
194C2×C8—268no—
195C2×C8—522no—
196C2×C8—524no—
197C4⋊C4—264no—
198C4⋊C4—524no—
199C22⋊C4—524no—
200C22⋊C4—528no—
201C42—134no—
202C42—134no—
203C42—132no—
204C42—132no—
205C42—264no—
206C42—262no—
207C42C2×#105712yes—
208C42#612212yes—
209C13#963811yescharacteristic, complemented, Sylow
210C23—24no—
211C23—44no—
212C23—44no—
213C23—42no—
214C23—42no—
215C23C2×C22⋊#26111yescharacteristic
216D4—28no—
217D4—416no—
218D4—44no—
219C2×C4—132no—
220C2×C4—132no—
221C2×C4—131no—
222C2×C4—131no—
223C2×C4—134no—
224C2×C4—132no—
225C2×C4—262no—
226C2×C4—262no—
227C2×C4—262no—
228C2×C4—524no—
229C2×C4—522no—
230C2×C4—1044no—
231C2×C4—1042no—
232C2×C4—1042no—
233C2×C4#8811514yes—
234C2×C4#8811614yes—
235C2×C4C22⋊#105714yes—
236C2×C4#8823812yes—
237C2×C4D4×#26112yes—
238C2×C4C22×#105711yescharacteristic
239C2×C4C2×#612211yescharacteristic
240C8—268no—
241C8—1042no—
242C22—48no—
243C22—44no—
244C22—84no—
245C22—82no—
246C22—82no—
247C22C2×#8811512yes—
248C22C2×#8811612yes—
249C22#1171914711yescharacteristic
250C22#1171915111yescharacteristic
251C22C2×C22⋊#105711yescharacteristic
252C4—132no—
253C4—131no—
254C4—131no—
255C4—264no—
256C4—262no—
257C4—1042no—
258C4D4⋊#105718yescomplemented
259C4D4×#105712yes—
260C4#1171914512yes—
261C2—84no—
262C2C2×D4⋊#105712yes—
263C2#1313018212yes—
264C2#1313095711yescharacteristic
265C2#1313096411yescharacteristic
266C2#1313097011yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC2×C4×C13C22×C8
FrattiniC22×C4C22×#261
Fitting, prime radicalC2×C13×#127C4
socleC23×C13C2×C22⋊C4
cosocleC2×C4×Dic13C23
hypercenterC2×#127#261
hypocenterC13#9638
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#127

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13130768C2semidirect
2. C42×#1057C2semidirect
3. C2×D4⋊#1057C2semidirect
23. C13×#127C8semidirect
41. C4×#1057D4semidirect
135. C4×C13D4⋊C8semidirect
150. #127#1057semidirect
209. C13#9638semidirect
258. C4D4⋊#1057semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#131307682
C42×#10572
C2×D4⋊#10572
#127×Dic132
#963813